Hours later, ABC News reported that the president and attorney general's relationship has "become so tense" that Sessions "at one point recently even suggested he could resign."
A Justice Department spokeswoman declined to comment to CNBC.
The developments followed a New York Times report that Trump "has grown sour on" Sessions, "blaming him for various troubles that have plagued the White House." The newspaper said that Trump has "fumed" over Sessions recusing himself from the FBI probe into alleged Russian interference in the 2016 election and possible ties between the Trump campaign and the Kremlin.
Trump targeted Sessions' Justice Department in a tweet Monday, saying that it should have "stayed with the original" version of what he called his "travel ban." Trump is pushing for the Supreme Court to reinstate a revised version of his executive order restricting travel from six predominantly Muslim countries.